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Simplifying 0.5(0.00342 + -0.004k) * 5 * 5 + 0.3333 * 0.000992 * 5 * 5 * 5 = 0 Reorder the terms for easier multiplication: 0.5 * 5 * 5(0.00342 + -0.004k) + 0.3333 * 0.000992 * 5 * 5 * 5 = 0 Multiply 0.5 * 5 2.5 * 5(0.00342 + -0.004k) + 0.3333 * 0.000992 * 5 * 5 * 5 = 0 Multiply 2.5 * 5 12.5(0.00342 + -0.004k) + 0.3333 * 0.000992 * 5 * 5 * 5 = 0 (0.00342 * 12.5 + -0.004k * 12.5) + 0.3333 * 0.000992 * 5 * 5 * 5 = 0 (0.04275 + -0.05k) + 0.3333 * 0.000992 * 5 * 5 * 5 = 0 Multiply 0.3333 * 0.000992 0.04275 + -0.05k + 0.0003306336 * 5 * 5 * 5 = 0 Multiply 0.0003306336 * 5 0.04275 + -0.05k + 0.001653168 * 5 * 5 = 0 Multiply 0.001653168 * 5 0.04275 + -0.05k + 0.00826584 * 5 = 0 Multiply 0.00826584 * 5 0.04275 + -0.05k + 0.0413292 = 0 Reorder the terms: 0.04275 + 0.0413292 + -0.05k = 0 Combine like terms: 0.04275 + 0.0413292 = 0.0840792 0.0840792 + -0.05k = 0 Solving 0.0840792 + -0.05k = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.0840792' to each side of the equation. 0.0840792 + -0.0840792 + -0.05k = 0 + -0.0840792 Combine like terms: 0.0840792 + -0.0840792 = 0.0000000 0.0000000 + -0.05k = 0 + -0.0840792 -0.05k = 0 + -0.0840792 Combine like terms: 0 + -0.0840792 = -0.0840792 -0.05k = -0.0840792 Divide each side by '-0.05'. k = 1.681584 Simplifying k = 1.681584
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